Description
Creates or tests for objects of class "Q4."Usage
Q4(q, ...) ## S3 method for class 'default':
Q4(q, theta = NULL, ...)
## S3 method for class 'SO3':
Q4(q, ...)
as.Q4(q)
is.Q4(q)
id.Q4
Arguments
q
object to be coerced or tested.
theta
vector of rotation angles.
Value
- as.Q4coerces its object into an Q4 type.
- is.Q4returns
TRUE or False
depending on whether its argument satifies the conditions
to be an quaternion. Namely, is four-dimensional and of
unit length. - Q4.defaultreturns an n-by-4 matrix
where each row is a quaternion constructed from axis U
and angle theta.
- Q4.SO3returns n-by-4 matrix
where each row is a quaternion constructed from the
corresponding rotation matrix.
format
id.Q4 is the identity rotation given by the matrix $[1,0,0,0]^\top$.Details
Construct a unit quaternion to represent a rotation.
Each quaternion can be interpreted as a rotation of some
reference frame about the axis U (of unit length) through
the angle theta. For each axis, U, and angle theta the
quaternion is formed through
$$q=[cos(\theta/2),sin(\theta/2)U]^\top.$$
If the theta element is left empty then the length of
each axis is taken to be the angle of rotation theta. If
an SO3 object is given then this function
will return the quaternion equivalent.